物理信息神经网络用于二维通道中圆柱绕流的黏弹性流体流动
Physics-informed neural networks for viscoelastic fluid flows around a cylinder in a two-dimensional channel
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中文总结 AI 辅助
本研究提出Cholesky-PINN方法，通过构象张量分解和稀疏数据同化解决高弹性Oldroyd-B流体绕流的高韦森伯格数问题，在Re=5-25及多圆柱阵列中稳定捕捉黏弹性尾流，避免传统CFD网格重划分。
中文摘要 AI 辅助
基于网格的流体动力学求解器通常面临繁琐的网格划分需求和不适定的反问题。物理信息神经网络（PINNs）提供了一种实用的无网格替代方案，但将其应用于高弹性Oldroyd-B流体会导致许多训练失败。高韦森伯格数问题（HWNP）由驻点附近的指数应力增长驱动，是一个主要问题，它会导致标准PINN优化器发散。为防止网络崩溃，我们对构象张量应用Cholesky分解。这一数学约束通过保证应力场正定来稳定梯度。除了数学稳定性之外，深度学习模型固有的谱偏差可能阻碍网络准确捕捉高弹性尾流结构。因此，我们使用稀疏数据同化将模型推向实际物理解。通过将物理损失与目标CFD数据点锚定，并利用迁移学习加速训练，我们成功地将网络推过非物理局部最小值。我们在单圆柱设置下，对雷诺数（Re）在5-25之间的圆柱几何绕流验证了这种Cholesky-PINN方法。此外，松弛时间（λ）从0.1增加到0.5以测试网络的稳定性。最后，我们将该框架扩展到复杂的3圆柱阵列，这证明了我们的构造实体几何方法完全绕过了传统CFD繁琐的重新网格划分步骤。该组合框架准确捕捉了尖锐的黏弹性尾流，为复杂流变学建模提供了稳定的计算工具。
英文摘要
Grid-based fluid dynamics solvers routinely struggle with exhaustive meshing demands and ill-posed inverse problems. A practical mesh-free alternative is given by Physics-informed neural networks (PINNs) but, applying them to highly elastic Oldroyd-B fluids results in many training failures. The High Weissenberg Number Problem (HWNP), driven by the exponential stress growth near stagnation points is a major issue, which causes standard PINN optimizers to diverge. To prevent the network from crashing, we apply a Cholesky decomposition to the conformation tensor. This mathematical constraint stabilizes the gradients by guaranteeing a positive-definite stress field. Beyond mathematical stability, the inherent spectral bias of deep learning models can hinder the network from accurately capturing the highly elastic wake structures. Therefore, we used sparse data assimilation to force the model toward the actual physical solution. By anchoring the physics loss with targeted CFD data points and accelerating training via transfer learning, we successfully pushed the network past non-physical local minima. We validated this Cholesky-PINN approach on flow past cylindrical geometries for Reynolds numbers (Re) between 5-25, for the single-cylinder setup. In addition, the relaxation time (λ) is increased from 0.1 to 0.5 to test the stability of the network. Finally, we scale the framework to a complex 3-cylinder array which proved our constructive solid geometry approach completely bypasses the tedious re-meshing steps of traditional CFD. The combined framework accurately captured sharp viscoelastic wakes, providing a stable computational tool for complex rheological modeling.
发表机构
- Maulana Azad National Institute of Technology (MANIT)（莫拉纳阿扎德国立理工学院）
机构由 AI 辅助整理，请以论文原文为准。
